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The modeling of the external disturbance vector of the earth from surface gravity anomaly data is discussed. The low frequency features of the signal are represented in spherical harmonic series. The recovery of the coefficients of the series from the given gravity anomalies is discussed focusing on the use of analytical continuation and ellipsoidal corrections to account for the earth's topography and ellipticity. The spectrum and data response of the spatial disturbance vector are studied to aid the design of models and experiments. The local models studied to complement the globally valid spherical harmonic model are (a) the residual topographic model (RTM), generated by integrating the gravitational influence of certain shallow topographic masses of assumed constant density; (b) the classical integral model, generated by integrating surface gravity anomalies that are assumed to refer to a mean level surface in the area; ( c) three versions of the Dirac approach to collocation, namely, those that imply the inversion of surface gravity anomaly data into gravity anomaly impulses Δg*, point masses μ*, and point dipoles μ-* on the Bjerhammar sphere; and finally (d) two versions of the least squares collocation (l.s.c.) approach, namely, those that are based on generating covariance functions from white noise distribution of gravity anomaly Δg* and of disturbing potential T* on the Bjerhammar sphere. The integral and collocation models are compared in their ability to recover the high frequency disturbance components implied by the RTM. Results indicate that the RTM itself should be used to model the high frequency signal variations whenever detailed (e.g., 1km x 1km) height data is available, since the integral and collocation models are limited in resolution through their use of gravity data with feasible spacing that can only be expected to be around 10 km x 10 km. The residual signal not already modeled by the RTM and spherical harmonic model can in most cases be accurately modeled by the integral model with mean topography accounted for. For high accuracies in mountainous areas, however, a collocation model should be used to account for the full variations of the topography, not just the mean topography. Matrix conditioning problems with the l.s.c. approach support preference to the Dirac systems for rigorous treatment of the topography at detailed (5' x 5') resolutions. [Some mathematical expressions are not fully represented in the metadata. Full text of abstract available in document.]